insideOutside: an accessible algorithm for classifying interior and exterior points, with applications in embryology

A crucial aspect of embryology is relating the position of individual cells to the broader geometry of the embryo. A classic example can be seen in the first cell-fate decision of the mouse embryo, where interior cells become inner cell mass and exterior cells become trophectoderm. Advances in image acquisition and processing technology used by quantitative immunofluorescence have resulted in the production of embryo images with increasingly rich spatial information that demand accessible analytical methods. Here, we describe a simple mathematical framework and an unsupervised machine learning approach for classifying interior and exterior points of a three-dimensional point-cloud. We benchmark our method to demonstrate that it yields higher classification rates for pre-implantation mouse embryos and greater accuracy when challenged with local surface concavities. This method should prove useful to experimentalists within and beyond embryology, with broader applications in the biological and life sciences.